Hierarchical Coding to Enable Scalability and Flexibility in Heterogeneous Cloud Storage

Abstract

In order to accommodate the ever-growing data from various, possibly independent, sources and the dynamic nature of data usage rates in practical applications, modern cloud data storage systems are required to be scalable, flexible, and heterogeneous. Codes with hierarchical locality have been intensively studied due to their effectiveness in reducing the average reading time in cloud storage. In this paper, we present the first codes with hierarchical locality that achieve scalability and flexibility in heterogeneous cloud storage using small field size. We propose a double-level construction utilizing so-called Cauchy Reed-Solomon codes. We then develop a triple-level construction based on this double-level code; this construction can be easily generalized into any hierarchical structure with a greater number of layers since it naturally achieves scalability in the cloud storage systems.

Hierarchical Hybrid Error Correction for Time-Sensitive Devices at the Edge

“…In this subsection, we introduce the extended Cauchy (EC) codes, which are the major component codes of the hierarchical codes proposed in [1], [18], [19]. We start with the definition of the essential ingredients of these codes, the so-called Cauchy matrices, and their extension, generalized Cauchy codes.…”

“…It has been proved in [1] that the Cauchy matrices are essential ingredients in a class of maximum distance separable (MDS) codes, as shown in Lemma 1.…”

“…Hierarchical codes that simultaneously support heterogeneity, scalability, and flexibility are first proposed and investigated in [1] for erasure-resilient cloud storage. However, erasure correction alone is not sufficient to allow these codes being directly used in the computational storage, where both failures (modeled as erasures) and errors can happen.…”

“…However, erasure correction alone is not sufficient to allow these codes being directly used in the computational storage, where both failures (modeled as erasures) and errors can happen. In this paper, we develop an efficient hybrid error correction algorithm of hierarchical codes proposed in [1] to correct both erasures and errors. The paper is organized as follows.…”

“…The paper is organized as follows. In Section II, we briefly introduce the constructions in [1] and their basic component codes, the EC codes. In Section III, we prove that the class of EC codes is different from existing codes in the literature, and it is strictly larger than the class of generalized Reed Solomon (GRS) codes and generalized Cauchy (GC) codes.…”